Overall, 3%
of
the students that apply to school get accepted. In a random group of 20 applicants, what is the probability that more than 3 are
accepted?

this is a binomial distribution with p = 0. 03, the probability for non of student get accepted is

(1-0.03)^20 =0.5438 , and 1 student got accepted is 20*(1-0.03)^19*0.03=0.3364, 2 students got accepted is 20*19/(2*1)*(1-0.03)^18*0.03^2 =0.0988, and 3 students got accepted is 20*19*18/(3*2*1)*(1-0.03)^17*0.03^3=.0183, so P(N>3) = 1-(P0+P1+P2+P3) = 1-(0.5438+0.3364+0.0988+0.0183) =0.0027